As summary. Any window/dialog beyond the main window opens fine, but on close of the dialog the entire program closes. Was getting bug report prompt, but when I went through the entire process, my submission was marked as a duplicate of a completely unrelated issue and I was informed that the crash is caused by phonon-backend-gstreamer.
I have now changed to phonon-backend-vlc, and the problem continues but does not instigate a bug report, implying that the trigger for the crash report is in fact related to gstreamer, but that the problem behavior is not.
This behavior started a few days ago, and a google search led me to this similar report: http://ubuntuforums.org/showthread.php?t=2157427
In an effort to provide more useful information I tried to generate a backtrace with gdb (since the bug report utility isn't starting) but it reports nothing when using 'thread apply all bt' and simply using 'bt' generates the response 'No stack.'
Here is the console output from the time when the program closes:

FIXME: handle dialog end. 
amarok: BEGIN: virtual TagDialog::~TagDialog() 
amarok: END__: virtual TagDialog::~TagDialog() [Took: 0s] 
The program 'amarok' received an X Window System error.
This probably reflects a bug in the program.
The error was 'BadWindow (invalid Window parameter)'.
  (Details: serial 4877 error_code 3 request_code 20 minor_code 0)
  (Note to programmers: normally, X errors are reported asynchronously;
   that is, you will receive the error a while after causing it.
   To debug your program, run it with the --sync command line
   option to change this behavior. You can then get a meaningful
   backtrace from your debugger if you break on the gdk_x_error() function.)

After hunting through my system for any other KDE specific applications, I have found that the same thing happens with all of them. That would seem to make this a KDE problem and not an Amarok specific one, and hopefully if anyone else starts reporting bugs in the next few days you can give them better info than the clearly preposterous attribution to gstreamer.